(or creatio ex nihilo)
Take a moment and look at the following sequence:
0 . . . ¼, ⅓, ½, 1, 2, 3, 4 . . . ∞
Note that the number 1 (one) is in the center and, as each number increases to the right, the inverse number decreases to the left.
If you multiply any of the corresponding inverse terms, the result is always 1.
2 × ½ = 1
3 × ⅓ = 1
4 × ¼ = 1
No matter how far you go, the result is always the same.
10100 × 1/10100 = 1
10100 = 1 with a hundred zeros after it.
If it had a billion zeros, it would make no difference—multiply any of the matching inverse terms and the result is always . . . 1. Of course, it seems obvious that multiplying any number by its reciprocal yields 1, but—
Therefore, when the increasing and decreasing series both reach their limits — ∞ and 0 — would not the result be the same if you multiply these two numbers?
∞ × 0 = 1
Ah, but there’s the rub. Are these two numbers really numbers?
This has been . . . Eine Kleine Naughtmusing.
HyC